November 5, 2008
OC
Big Idea: Many things in our world are mathematically similar and we can use this to understand and describe the world around us.
Essential Question: How can I use math to check if two figures are similar?
Notes: The change in area between similar figure is the scale times 2.
The change in area between similar figures is the scale factor.
Question A: Start with four copies of one of the shapes. Try to find a way to put the four copies together-with no overlap and no holes-to make a larger, similar shape. If you are successful, make a sketch showing how the four shapes (rep-tiles) fit together, and give the scale factor from the original shape to the new shape. Repeat this process with each shape.
Answer A: Question B: For each rep-tile you found in part A, try to find a different way to arrange the copies to get a similar shape. Sketch each new arrangement. How does the scale factor for each new arrangement compare to the scale factor for the first arrangement?
Answer B: Question C: Start with one of the rep-tiles you found in part A. Try to add copies of the rep-tile to this shape to make the next-largest similar shape. If you are successful, make a sketch showing how the copies fit together. Repeat this process with each rep-tile you found in part A.
Answer C:
Follow Up
Question 1: Examine your work from Problem 3.2 carefully. What is the relationship between the scale factor and the number of copies of an original shape needed to make a larger, similar shape?
Answer 1: The scale factor squared it self is the area of the shape.
Question 2: Is the number of copies of an original shape used to make a new shape related to the side lengths or the area of the new shape?
Answer 2: The number of copies of an original is related to the area because it is squared.
OC
Big Idea: Many things in our world are mathematically similar and we can use this to understand and describe the world around us.
Essential Question: How can I use math to check if two figures are similar?
Notes: The change in area between similar figure is the scale times 2.
The change in area between similar figures is the scale factor.
Question A: Start with four copies of one of the shapes. Try to find a way to put the four copies together-with no overlap and no holes-to make a larger, similar shape. If you are successful, make a sketch showing how the four shapes (rep-tiles) fit together, and give the scale factor from the original shape to the new shape. Repeat this process with each shape.
Answer A:
Question B: For each rep-tile you found in part A, try to find a different way to arrange the copies to get a similar shape. Sketch each new arrangement. How does the scale factor for each new arrangement compare to the scale factor for the first arrangement?
Answer B:
Question C: Start with one of the rep-tiles you found in part A. Try to add copies of the rep-tile to this shape to make the next-largest similar shape. If you are successful, make a sketch showing how the copies fit together. Repeat this process with each rep-tile you found in part A.
Answer C:
Follow Up
Question 1: Examine your work from Problem 3.2 carefully. What is the relationship between the scale factor and the number of copies of an original shape needed to make a larger, similar shape?
Answer 1: The scale factor squared it self is the area of the shape.
Question 2: Is the number of copies of an original shape used to make a new shape related to the side lengths or the area of the new shape?
Answer 2: The number of copies of an original is related to the area because it is squared.